For example, consider a situation where an input signal is processed on a frame basis, and each frame contains N samples, as shown in FIG. 1. The input signal is represented as XO(n) (n=1, 2, . . . , N). The maximum allowable order of the PARCOR coefficient is Pmax.
A linear prediction analysis part 901 calculates the PARCOR coefficients of the first order to the predetermined maximum, Pmax-th order, KO(1), KO(2), . . . , KO(Pmax) from the input signal XO(n) according to the Levinson-Durbin method, the Burg method or the like, and outputs an optimal order PO and a PARCOR coefficient sequence KO=(KO(1), KO(2), . . . , KO(PO)) of the PARCOR coefficients of the first order to the PO-th order determined according to some method (see Patent literature 1, for example).
A quantization part 903 quantizes the PARCOR coefficient sequence KO and outputs a quantized PARCOR coefficient sequence K′O=(K′O(1), K′O(2), . . . , K′O(PO)). A reverse conversion part 905 converts the quantized PARCOR coefficient sequence K′O into a linear prediction coefficient sequence a′O=(a′O(1), a′O(2), . . . , a′O(PO)), and outputs the linear prediction coefficient sequence a′O=(a′O(1), a′O(2), . . . , a′O(PO)). A filter 907 performs PO-th order filtering of the input signal XO(n) (n=1, 2, . . . , N) using the linear prediction coefficient sequence a′O=(a′O(1), a′O(2), . . . , a′O(PO)) as a filter factor according to the following formula (1), thereby determining a prediction residual eO(n) (n=1, 2, . . . , N). Note that aO′(0)=1. In the following formula, the symbol “x” represents a multiplication.
                              eo          ⁡                      (            n            )                          =                              ∑                          i              =              0                        Po                    ⁢                                    a              ′                        ⁢                          o              ⁡                              (                i                )                                      ×                          Xo              ⁡                              (                                  n                  -                  i                                )                                                                        (        1        )            
A residual coding part 911 performs entropy coding of the prediction residual eO(n), for example, and outputs a residual code CeO. A coefficient coding part 909 codes the optimal order PO and the quantized PARCOR coefficient sequence K′O=(K′O(1), K′(2), . . . , K′O(PO)) and outputs a coefficient code CkO. A code synthesis part 913 combines the residual code CeO and the coefficient code CkO and outputs the resulting synthesis code CaO.
The quantization part 903 quantizes the PARCOR coefficient for efficient code transmission.
FIG. 2 shows an example of linear quantization of the PARCOR coefficient according to a prior art. Each PARCOR coefficient in the PARCOR coefficient sequence KO assumes a real number value falling within a range from −1 to +1. Assuming that each PARCOR coefficient is calculated with a 16-bit precision, and the value obtained by multiplying the PARCOR coefficient by 32768 is represented by a signed 16-bit integer, the PARCOR coefficient can assume a value falling within a range from −32768 to +32767. That is, −(32768/32768) =−1 corresponds to a signed 16-bit integer that represents −32768, and +−(32767/32768) ≈+1 corresponds to a signed 16-bit integer that represents +32767. The signed 16-bit integer values are linearly quantized with four bits. Specifically, of the bits of the signed 16-bit integers that represent the values obtained by multiplying the PARCOR coefficients in the PARCOR coefficient sequence KO by 32768, the higher order four bits are maintained, and the remaining lower order twelve bits are padded with 0. Then, the resulting value is divided by 32768, resulting in a quantized PARCOR coefficient sequence K′O. The quantized PARCOR coefficients in the quantized PARCOR coefficient sequence K′O are 4-bit precision values, and therefore, the error due to the quantization is significant compared with the 16-bit precision. However, the code amount required to represent each quantized PARCOR coefficient in the quantized PARCOR coefficient sequence K′O is only 4 bits. The quantization precision can be determined based on the trade-off between the quantization error and the code amount.
According to a conventional audio coding involving some loss (distortion), in order to prevent an audible sound quality degradation in the case where the PARCOR coefficient is coded with a small code amount, the PARCOR coefficient is quantized by using the spectral distortion as a measure. As disclosed in Non-patent literatures 1 to 3, nonlinear quantization is performed by using an arc sin function or a tan h function, and the bit allocation is varied depending on the order. As an alternative, as disclosed in Non-patent literature 4, in lossless coding of an audio signal according to MPEG-4 ALS, a nonlinear function involving a radical sign is used. In any case, to prevent the prediction residual eO(n) from increasing, the PARCOR coefficient sequence KO is quantized by quantizing PARCOR coefficients close to −1 and +1 that have higher sensitivities (more significant errors) with higher precisions and quantizing PARCOR coefficients close to 0 with lower precisions. However, the nonlinear quantization requires a more complicated process than the linear quantization.